The required absolute value equation is |2x - 11| = 7. Where x = 2 and x = 9.
<h3>What is the solution for an absolute value equation?</h3>
The absolute value equation is represented by |x - a| = b.
Then, its solution set is calculated by
x - a = +b and x - a = -b
Where a and b are real values.
<h3>Calculation:</h3>
It is given that,
The solutions for an absolute value equation are x = 2 and x = 9;
So, the required equation is
|x - a| = b
Then,
for x = 2; the equation is |2 - a| = b
for x = 9; the equation is |9 - a| = b
Since it is an absolute value, one root is obtained by positive operation and the other is obtained by negative operation.
So, consider
2 - a = b ...(1)
9 - a = -b ...(2)
By simplifying these two equations, we get
a = 11/2
So, b = ± 7/2
Thus, substituting these values in the general form results in the required equations as
x - a = ±b
⇒ x - 11/2 = ± 7/2
⇒ 2x - 11 = ±7
(Since it is ± taking absolute value)
⇒ |2x - 11| = 7
Therefore, the required absolute value equation is |2x - 11| = 7.
Check:
|2x - 11| = 7
⇒ 2x - 11 = 7 and 2x - 11 = -7
⇒ 2x = 7 + 11 and 2x = -7 + 11
⇒ 2x = 18 and 2x = 4
⇒ x = 9 and x = 2
Learn more about an absolute value equation here:
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